Show that the differential equation
`xylog(y/x)dx+{y^(2)-x^(2)log(y/x)}dy=0` is homogeneous and solve it.

Explanation

To solve the given differential equation \( xy \log\left(\frac{y}{x}\right)dx + \left(y^2 - x^2 \log\left(\frac{y}{x}\right)\right)dy = 0 \), we will follow these steps:

### Step 1: Show that the differential equation is homogeneous

A differential equation is homogeneous if it can be expressed in the form \( M(x, y)dx + N(x, y)dy = 0 \) where both \( M \) and \( N \) are homogeneous functions of the same degree.

Given:
\[
...